May 27, 2024Open Access

Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube

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Authors

LALaura AngelonıUniversity of Perugia DCDanilo CostarellıUniversity of Perugia CDChiara DarielliUniversity of Florence

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Implication

Theoretical analysis reveals uniform convergence and quantitative approximation bounds on the unit hypercube, highlighting exact preservation of multidimensional exponential functions.

Key Points

The new family of multidimensional exponential polynomials achieves uniform convergence on the hypercube while fixing the exponential function and its square.
Theoretical analysis establishes quantitative bounds on the approximation error using two distinct convergence methods and the modulus of continuity.
These findings support refined function approximation in multidimensional domains, expanding analytical tools for exponential polynomials on compact sets.

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Angelonı et al. (2024) studied this question.

synapsesocial.com/papers/68e68593b6db64358760de72 https://doi.org/10.48550/arxiv.2405.16935

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Implication

Theoretical analysis reveals uniform convergence and quantitative approximation bounds on the unit hypercube, highlighting exact preservation of multidimensional exponential functions.

Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube

Discussion

Member takes

Implication

Key Points

Cite This Study

Approximation processes by multidimensional Bernstein-type exponential polynomials on the hypercube

Discussion

Member takes

Implication

Key Points

Cite This Study

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